Here presented are the definitions of （c）-Riordan arrays and （c）-Bell polynomials which are extensions of the classical Riordan arrays and Bell polynomials. The characterization of （c）-Riordan arrays by means of...Here presented are the definitions of （c）-Riordan arrays and （c）-Bell polynomials which are extensions of the classical Riordan arrays and Bell polynomials. The characterization of （c）-Riordan arrays by means of the A- and Z-sequences is given, which corresponds to a horizontal construction of a （c）-Riordan array rather than its definition approach through column generating functions. There exists a one-to-one correspondence between GegenbauerHumbert-type polynomial sequences and the set of （c）-Riordan arrays, which generates the sequence characterization of Gegenbauer-Humbert-type polynomial sequences. The sequence characterization is applied to construct readily a （c）-Riordan array. In addition, subgrouping of （c）-Riordan arrays by using the characterizations is discussed. The （c）-Bell polynomials and its identities by means of convolution families are also studied. Finally, the characterization of （c）-Pdordan arrays in terms of the convolution families and （c）-Bell polynomials is presented.展开更多
文摘Here presented are the definitions of （c）-Riordan arrays and （c）-Bell polynomials which are extensions of the classical Riordan arrays and Bell polynomials. The characterization of （c）-Riordan arrays by means of the A- and Z-sequences is given, which corresponds to a horizontal construction of a （c）-Riordan array rather than its definition approach through column generating functions. There exists a one-to-one correspondence between GegenbauerHumbert-type polynomial sequences and the set of （c）-Riordan arrays, which generates the sequence characterization of Gegenbauer-Humbert-type polynomial sequences. The sequence characterization is applied to construct readily a （c）-Riordan array. In addition, subgrouping of （c）-Riordan arrays by using the characterizations is discussed. The （c）-Bell polynomials and its identities by means of convolution families are also studied. Finally, the characterization of （c）-Pdordan arrays in terms of the convolution families and （c）-Bell polynomials is presented.
